论文标题
连续量子场理论的变分神经网络ANSATZ
Variational Neural-Network Ansatz for Continuum Quantum Field Theory
论文作者
论文摘要
可以追溯到Feynman的物理学家感叹将变异原理应用于量子场理论的困难。在非相关的量子场理论中，挑战是在无限的许多$ n $粒子波函数上进行参数化和优化，该功能包括该州的Fock空间表示。在这里，我们通过引入神经网络量子场状态来解决这个问题，这是一个深入学习的ANSATZ，它可以将变分原理应用于连续体中的非相关量子场理论。我们的ANSATZ使用Deep Sets神经网络体系结构来同时参数化包含量子场状态的所有$ N $粒子波函数。我们采用ANSATZ来近似各种领域理论的基础状态，包括不均匀的系统和具有远距离相互作用的系统，从而证明了一种强大的新工具来探测量子场理论。
Physicists dating back to Feynman have lamented the difficulties of applying the variational principle to quantum field theories. In non-relativistic quantum field theories, the challenge is to parameterize and optimize over the infinitely many $n$-particle wave functions comprising the state's Fock space representation. Here we approach this problem by introducing neural-network quantum field states, a deep learning ansatz that enables application of the variational principle to non-relativistic quantum field theories in the continuum. Our ansatz uses the Deep Sets neural network architecture to simultaneously parameterize all of the $n$-particle wave functions comprising a quantum field state. We employ our ansatz to approximate ground states of various field theories, including an inhomogeneous system and a system with long-range interactions, thus demonstrating a powerful new tool for probing quantum field theories.
